Edge modes of gravity. Part I. Corner potentials and charges

• Published in: The journal of high energy physics Vol. 2020; no. 11; pp. 1 - 52
• Main Authors: Freidel, Laurent, Geiller, Marc, Pranzetti, Daniele
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2020; Springer Nature B.V; Springer; SpringerOpen
• Subjects: Algebra; Classical and Quantum Gravitation; Classical Theories of Gravity; Elementary Particles; Gauge Symmetry; Gravity; High energy physics; High Energy Physics - Theory; Mathematical analysis; Models of Quantum Gravity; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum gravity; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Representations; Space-Time Sym- metries; String Theory; Symmetry; Classical Theories of Gravity; Space-Time Sym- metries; Gauge Symmetry; Models of Quantum Gravity; symmetry: algebra; tetrad; gravitation: Einstein-Cartan; quantum gravity; structure; quantum geometry; differential geometry; potential: symplectic; quantization
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP11(2020)026

A bstract This is the first paper in a series devoted to understanding the classical and quantum nature of edge modes and symmetries in gravitational systems. The goal of this analysis is to: i) achieve a clear understanding of how different formulations of gravity provide non-trivial representations of different sectors of the corner symmetry algebra, and ii) set the foundations of a new proposal for states of quantum geometry as representation states of this corner symmetry algebra. In this first paper we explain how different formulations of gravity, in both metric and tetrad variables, share the same bulk symplectic structure but differ at the corner, and in turn lead to inequivalent representations of the corner symmetry algebra. This provides an organizing criterion for formulations of gravity depending on how big the physical symmetry group that is non-trivially represented at the corner is. This principle can be used as a “treasure map” revealing new clues and routes in the quest for quantum gravity. Building up on these results, we perform a detailed analysis of the corner pre-symplectic potential and symmetries of Einstein-Cartan-Holst gravity in [1], use this to provide a new look at the simplicity constraints in [ 2 ], and tackle the quantization in [ 3 ].